This counter-intuitive result can be understood by realising that core nodes have very high degree, so the sum of degrees in the core, \(T_{a}\) , will therefore be very large. The diagonal contribution from the core-core part \(Q_{aa} = \Sigma _{aa} - \frac{T_a^2}{2E}\)  is likely to be large and negative, reducing the modularity \(Q(B)\)  significantly if \(B_{aa} = 1\) . By assigning a negative sign to the core nodes \(Q(B)\)  is increased. The result is analogous to [1]}, certain block patterns may intuitively appear to be optimal, but under the configuration model they are not, due to the importance of degree correlations.
